Choose: 33% Off or 50% More

The linked article in The Economist (http://www.economist.com/node/21557801) justifies that when it comes to discounting, the general public are bad at math.  The mathematical principal involved is this: discounting takes a percentage off of a large number, but giving a buy-on-get-one, gift with purchase or an upgrade involves percentages compared to a lower number.  The latter results in a larger more appealing percentage.

Here is a chart assuming that you’re using a half-carat ring worth $3,000 as a benchmark, but offering a larger more valuable ring at the same $3,000 price.

New Ring Value	Increase in Value	Discount to $3K
$4,000	33%	25%
$4,500	50%	33%
$5,000	66%	40%
$6,000	100%	50%

The third column assumes that you’re taking the more valuable ring and discounting it to achieve a $3,000 price.  Notice how much larger the numbers are in the second column than the third?

If you’re running a promotion where you offer a $5,000 2/3ct solitaire for the price of a $3,000 1/2ct solitaire, you could use three different numbers.  You could boast a 33% larger diamond for the same price, 40% discount or 66% more value.  The Economist article would suggest that you’ll get the best response by using the largest number.